Multi-reflecting mass spectrometers, either time-of-flight (MR-TOF MS), open traps, or electrostatic traps (E-trap), comprise gridless ion mirrors to arrange isochronous motion of ion packets, essentially independent of ion energy and spatial spreads.
An important class of ion mirrors for multi-reflecting mass spectrometers is represented by mirrors which are substantially elongated in one transverse direction Z to form a two-dimensional electrostatic field. This field can have either planar or hollow cylindrical symmetry. SU1725289, incorporated herein by reference, introduces an MR TOF MS with ion mirrors of planar symmetry. Except Z-edges, the electrostatic field is two-dimensional E(X, Y), i.e. essentially independent of the Cartesian coordinate Z Ions move along zigzag trajectories, being injected at small angle to X-axis, periodically reflected from the mirrors in the X-direction, spatially focused in the Y-direction, and slowly drifting in the Z-direction. U.S. Pat. No. 7,196,324, GB2476964, GB2477007, WO2011086430, and co-pending application 223322-313911,incorporated herein by reference, disclose multi-reflecting analyzers with hollow cylindrical mirrors formed by two sets of coaxial ring electrodes. Contrary to planar mirrors, cylindrical mirrors eliminate Z-edges, thus forming electrostatic field completely independent on the azimuthal Z-direction. The analyzer provides a compact folding of ion path per instrument size. However, when arranging zigzag ion trajectories, the ion path deviates from a cylindrical surface, which demands for ion mirrors being highly isochronous relative to radial Y-displacements.
Electrostatic multi-reflecting analyzers with two-dimensional ion mirrors of both—planar and hollow cylindrical geometry are disclosed for use as time-of-flight analyzers (SU1725289, U.S. Pat. No. 7,385,187), open traps (GB2478300, WO2011107836), and electrostatic traps (GB2476964, GB2477007, WO2011086430). While in time-of-flight (TOF) analyzers ion packets travel towards a fast response detector along a fixed path, in electrostatic traps, the ion packets are trapped indefinitely. They keep reflecting while being detected by image current detector. Open electrostatic traps could be considered as a hybrid between TOF and traps. Ions reach a detector after a loosely defined number of reflections within some span in the number of reflections.
Multi-reflecting time-of-flight mass spectrometers can be combined with a set of periodic lenses to confine ions in the Z-direction, as disclosed in GB2403063 and U.S. Pat. No. 7,385,187,incorporated herein by references. US2011186729, incorporated herein by reference, discloses quasi-planar ion mirrors, in which the electrostatic field of planar symmetry is superimposed with a weak field spatially periodic in the Z-direction to provide ion confinement in this direction. Such periodic field, by itself or in combination with periodic lenses, allows significant reducing of flight time distortions due to the spatial Z-spread in ion bunches. GB2476964, GB2477007, WO2011086430, incorporated by reference, disclose periodic lens in the tangential direction within cylindrical hollow analyzers.
The general trend in design of multi-reflecting mass spectrometers is to minimize the effect of ion packet broadening during periodic ion motion between the mirrors in order to increase the mass resolving power of the spectrometer at given energy tolerance and phase space acceptance, i.e. acceptance of initial spatial, angular, and energy spreads of ion packets. In order to improve the energy tolerance of the mass analyzer, U.S. Pat. No. 4,731,532, incorporated herein by reference, discloses a gridless ion mirror with a purely retarding field which provides for second-order focusing of the flight time T with respect to kinetic energy K, i.e. dT/dK=d2T/dK2=0. Since present invention is primarily concerned with analyzer isochronicity we will be referring time-per-energy focusing as “energy focusing”. In the paper by A. Verenchikov et al., Technical Physics, v. 50, N1, 2005, p. 73-81, incorporated herein by references, planar ion mirrors are described with an accelerating potential at one of the mirror electrodes, which provide for third-order energy focusing, i.e. for dT/dK=d2T/dK2=d3T/dK3=0. Co-pending application 223322-318705, incorporated herein by reference, discloses gridless ion mirrors of either planar or hollow cylindrical geometry, possessing fourth (d4T/dK4=0) and fifth (d5T/dK5=0) order energy focusing. Achieving high order of energy focusing allows increasing the energy tolerance of the mass analyzer to >10% at mass resolving power above 100,000.
Since in gridless ion mirrors due to an inhomogeneous field structure ion flight time in general depends not only on ion energy but also on ion initial coordinate and direction of motion, it is important to design ion mirrors such to provide for periodic focusing of the flight time with respect to the spatial spread of ion packets. In general, for two dimensional and Z-independent fields with X-direction for ion reflections, the flight time T through the analyzer depends on ion kinetic energy K, initial spatial coordinate Y0 and angular coordinate b0 (b=dY/dX). At small deviations of initial ion parameters the time-of-flight deviations can be represented by the Taylor expansion:
  y  =                    (                  T          |          δ                )            ⁢      δ        +                  (                  T          |          δδ                )            ⁢              δ        2              +                  (                  T          |          δδδ                )            ⁢              δ        3              +                  (                  T          |          δδδδ                )            ⁢              δ        4              +                  (                  T          |          δδδδδ                )            ⁢              δ        5              +    …    +                  (                  T          |          yy                )            ⁢              y        0        2              +                  (                  T          |          yb                )            ⁢              y        0            ⁢              b        0              +                  (                  T          |          bb                )            ⁢              b        0        2              +                  (                  T          |                      yy            ⁢                                                  ⁢            δ                          )            ⁢              y        0        2            ⁢      δ        +                  (                  T          |                      yb            ⁢                                                  ⁢            δ                          )            ⁢              y        0            ⁢              b        0            ⁢      δ        +                  (                  T          |                      bb            ⁢                                                  ⁢            δ                          )            ⁢              b        0        2            ⁢      δ        +    …  where t=(T−T0)/T0 is the relative flight time deviation, T0 is the flight time corresponding to an ion with zero initial coordinates Y0=B0=0 and with the mean kinetic energy value K0, δ=(K−K0)/K0 is the relative energy deviation, and y=Y/H is the coordinate normalized to the window height H of the ion mirror. The expansion (aberration) coefficients ( . . . | . . . ) are normalized derivatives: (t|δ)=dt/dδ, (t|δδ)=(½)d2t/dδ2 etc. N-th order energy focusing means that all coefficients at the pure powers of δ up to N-th power inclusively are zeroes. The second order spatial focusing (i.e. time-of-flight focusing with respect to spatial and energy spreads) means that (t|yy)=(t|yb)=(t|bb)=0, because the mixed second order terms (t|yδ) and (t|bδ) vanish due to the system symmetry with respect to the plane Y=0.
The paper by M. Yavor et al., Physics Procedia, v. 1 N1, 2008, p. 391-400, incorporated herein by reference, provides details of geometry and potentials for planar ion mirrors which simultaneously provide the third order energy focusing, second order spatial focusing and geometrical focusing in Y-direction. In such analyzers, the broadening of ion packets in the mirror fields is dominated by so-called “mixed” third order aberrations due to both spatial and energy spreads, i.e. terms (t|yyδ)y02δ, (t|ybδ)y0b0δ and (t|bbδ)b02δ, because the rest third order aberrations vanish due to the system symmetry with respect to the plane Y=0. These terms are responsible for deterioration of the resolving power of multi-reflection mass spectrometers at both FWHM level and even more severely at the 10% peak height level. This deterioration is especially noticeable in hollow cylindrical analyzers in which ions are periodically shifted in radial Y-direction from the “ideal” cylindrical surface of ion motion, as well as in planar mass analyzers with periodic lenses, in which ions are injected with a large enough Y-spread through a “double orthogonal” accelerator described in US2007176090, incorporated herein by reference.
As described in the co-pending application 223322-318705, incorporated herein by reference, the order of energy focusing can be increased by optimizing the electrostatic potential distribution in the region of ion reflection. The improvement is reached by increasing the number of mirror electrodes with different electrode potentials and choosing sufficiently thin electrodes in the region of ion reflection. This strategy of design, however, fails in case one wants to achieve high order energy focusing simultaneously with high order spatial focusing. Up to fifth-order energy focusing may be achieved in combination with the second-order spatial focusing. To obtain third-order energy focusing in combination with the third-order spatial focusing one has to increase the width of the mirror electrode with accelerating potential, though such geometry modification causes a negative consequence of reducing the spatial acceptance of the ion mirror. However, our own thorough numerical simulations of gridless ion mirrors show that no straightforward steps like increasing the number of mirror electrodes, splitting them into parts with introducing more independent electrode voltages, varying their widths and shapes and other similar means do not lead to elimination of the mixed (energy-spatial) third order aberrations in ion mirrors with the fourth and higher order of energy focusing. Using the above mentioned optimization procedures one can reach high-order energy isochronicity, however, at a cost of increasing mixed third order aberrations. In other words, increasing the energy acceptance leads to reduction of the spatial acceptance.
Thus, prior art ion mirrors possess either high energy acceptance or high spatial acceptance but not both at the same time. Therefore, there is a need for improving the spatial phase space acceptance of ion mirrors possessing high energy tolerance, i.e. flight time focusing with respect to energy of fourth and higher orders.